Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1212 conjugacy classes of subgroups; only the 509 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 509 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Frattini | C22 | C24×D89 |
| Fitting | C22×C42×C89 | C2 |
| hypercenter | C22×C42 | D89 |
| hypocenter | C89 | #3444 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19152155 | C2 | semidirect |
| 2. #19152148 | C2 | semidirect |
| 3. #19152132 | C2 | semidirect |
| 4. #19152109 | C2 | semidirect |
| 5. C4×#13083574 | C2 | semidirect |
| 6. C22×C42×C89 | C2 | semidirect |
| 8. #15668012 | C22 | semidirect |
| 9. #15668009 | C22 | semidirect |
| 10. #15668006 | C22 | semidirect |
| 11. #15668004 | C22 | semidirect |
| 12. #15668000 | C22 | semidirect |
| 17. C4×Dic178 | C22 | semidirect |
| 18. C4×D356 | C22 | semidirect |
| 21. #15667969 | C22 | semidirect |
| 22. C42×D89 | C22 | semidirect |
| 55. C2×C4×C89 | #41 | semidirect |
| 77. C89 | #3444 | semidirect |
| 83. C22×C42 | D89 | semidirect |
| 137. C2×C4 | #13083574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152155 | 2 |
| #19152148 | 2 |
| #19152132 | 2 |
| #19152109 | 2 |
| C4×#13083574 | 2 |
| C22×C42×C89 | 2 |
| #3444 | 89 |